Introduction to Tropical Geometry and Elements of Toric Geometry

a.a. 2024/25

Academic coordinator: Stefano Urbinati

Period: second semester

Duration: 28 hours

Program:

  • Definition of tropical geometry
  • Basic concepts of algebraic geometry
  • Introduction to tropical numbers
  • Tropical monomials and affine integral geometry
  • Amoebas of affine algebraic varieties and their limits
  • Introduction to polyhedral geometry
  • The balancing condition
  • Tropical plane curves
  • Tropical toric varieties
  • Tropical projective space and projective hypersurfaces
  • Tropical cycles, subspaces, and stable intersection
  • Practical examples and applications
  • Final sessions chosen by the students, including participant presentations